The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

Question

The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is (A) 120 cm (B) 140 cm (C) 80 cm (D) 100 cm

Tardigrade Admin · Accepted Answer

For closed organ pipe, fundamental frequency is given by

v_{c} = \frac{v}{4 l}

For open organ pipe, fundamental frequency is given by

v_{o} = \frac{v}{2 l ^{'}}

2^{nd}

overtone of open organ pipe

v^{'} = 3 v_{o}; v^{'} = \frac{3 v}{2 l ^{'}}

According to question,

v_{c} = v^{'}

\frac{v}{4 l} = \frac{3 v}{2 l ^{'}}

l^{'} = 6 l

Here,

l = 20 c m, l^{'} =

?

∴ l^{'} = 6 \times 20 = 120 c m

Q. The fundamental frequency of a closed organ pipe of length 20cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

120 cm

140 cm

80 cm

100 cm

Q. The fundamental frequency of a closed organ pipe of length $20 c m$ is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is